Termination detection constitutes one of the basic problems of distributed computing and many distributed algorithms have been proposed to solve it. These algorithms differ in the way they ensure consistency of the detection and in the assumptions they do concerning behaviour of channels (FIFO or not, bounded delay or asynchronous, etc.) But all these algorithms consider a very simple model for underlying application programs : for processes of such programs non-deterministic constructs are allowed but each receive statement (request) concerns only one message at a time. In this paper a more realistic and very general model of distributed computing is first presented. This model allows a request (receive statement) to be atomic on several messages and to obey and/or/and-or/k out of n/etc request types. These types are abstracted by the notion of an activation condition. Within this framework two definitions of termination are proposed and discussed. Then, accordingly, two distributed algorithms to detect these terminations are presented and evaluated, they differ in the information they use and in the time they need to claim termination.